Real-time inference and extrapolation with Time-Conditioned UNet: Applications in hypersonic flows, incompressible flows, and global temperature forecasting
Year: 2025
Type: article
Abstract: Neural Operators are fast and accurate surrogates for nonlinear mappings between functional spaces within training domains. Extrapolation beyond the training domain remains a grand challenge across all application areas. We present Time-Conditioned UNet (TC-UNet) as an operator learning method to solve time-dependent PDEs continuously in time without any temporal discretization, including in extrapolation scenarios. TC-UNet incorporates the temporal evolution of the PDE into its architecture by combining a parameter conditioning approach with the attention mechanism from the Transformer architecture. After training, TC-UNet makes real-time inferences on an arbitrary temporal grid. We demonstrate its extrapolation capability on a climate problem by estimating the global temperature for several years and also for inviscid hypersonic flow around a double cone. We propose different training strategies involving temporal bundling and sub-sampling. We demonstrate performance improvements for several benchmarks, performing extrapolation for long time intervals and zero-shot super-resolution time. • We present TC-UNet, a neural operator for arbitrary temporal resolution inference. • TC-UNet outperforms FNO and UNet in zero-shot temporal super-resolution tasks. • TC-UNet is stable in modeling hypersonic flows with high spatiotemporal gradients. • Sensitivity analysis demonstrates TC-UNet as very stable to noise. • TC-UNet extrapolates better in time than regular UNet without time-conditioning.
Institutions: Tel Aviv University, Brown University
Language: English
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $4,830
OpenAlex ID: W4409448188